Superconductivity has remained an active area of research for over 100 years. The interplay between superconductivity and other phases of matter continues to be an excellent avenue to explore novel physical phenomena. This thesis is a report on materials in which electrons form Cooper pairs and have symmetry properties that allow for the exhibition of novel phenomena in the superconducting state. The main focus of this thesis is the interplay between superconductivity and topology. In the first Chapter an introduction to topology is given. This is followed by the experimental details in Chapter 2 and the theoretical background in Chapter 3. The type-II Dirac semimetal PdTe2 is a type-I superconductor with unusual superconductivity in the surface sheath. The results of relaxation calorimetry to investigate the intermediate state of PdTe2 is given in Chapter 4. A doping study to tune the superconductivity of PdTe2 to that of the second kind that was investigated by relaxation calorimetry and ac suceptibility is given in Chapter 5. The angle-dependent magnetotransport study on the layered type-II superconductor LaO0.8F0.2BiS2−xSex (x = 0.5 and 1.0), with breaking of the local inversion symmetry possibly leading to the large anisotropy in the upper critical field is presented in Chapter 6. A study on the effects of pressure on the superconductivity in PdTe2 is given in Chapter 7.